In transmission systems, Half-Duplex (HD) transmission refers to transmitting and receiving signals, but either not at the same time or not over the same frequency resource. In contrast, with Full-Duplex (FD) transmission, the signals are transmitted and received simultaneously over the same frequency resource at the same time. FD transmission has the potential to provide approximately double sum-rate improvements over HD transmission. However, FD transmission suffers from high self-interference. Self-interference refers to the noise added to the detected received signal due to a portion of the device transmitted signal propagating into the receiver of the same device. Transmission systems can also employ a Multiple-Input-Multiple-Output (MIMO) scheme where multiple antennas in a device are used at both the transmitter and receiver to improve communication performance. The MIMO technique allows high data throughput and link range in comparison to single antenna transmission techniques. This is achieved by spreading the same total transmit power over the multiple antennas to achieve an array gain that improves the spectral efficiency (more bits per second per hertz of bandwidth) and/or to achieve a diversity gain that improves the link reliability. A transmission system, such as in current and fifth generation (5G) radio access networks (RANs) or in WiFi networks, can benefit from implementing both MIMO and FD transmission schemes to achieve high transmission rates and throughput. However, the large rate and throughput requirements make device communications highly susceptible to noise, particularly the high self-interference noise associated with FD transmissions. Therefore, there is a need for effective schemes to realize the benefits of FD operation with the MIMO scheme and mitigate self-interference in such systems.